US20020174086A1 - Decision making in classification problems - Google Patents

Abstract

A method of classifying samples to one of a number of predetermined classes involves using a number of class models or classifiers to form order statistic for each classifier. A linear combination of the order statistic (L-statistic) is calculated to determine the confidence of that particular classifier, both in general and for that particular sample. Relative weights are then derived from these confidences, and used to calculate a weighted summation across all classifiers for each class of the likelihoods that a sample belongs to that class. The sample is classified in the class which has the associated weighted summation which is greatest in value.

Description

FIELD OF THE INVENTION
• The invention relates to decision making in classification problems and relates particularly, though not exclusively, to improved methods of classification in decision fusion applications.[0001]
BACKGROUND OF THE INVENTION
• Decision fusion is a widely used technique for several kinds of classification applications such as, for example, medical imaging, biometric verification, signature or fingerprint recognition, robot vision, speech recognition, image retrieval, expert systems etc.[0002]
• Generally, in decision fusion applications, multiple classifiers (or experts) perform separate classification experiments on respective data sets, and consequently designate a nominated class as correct. The classifier decisions are then combined in a predetermined selection strategy to arrive at the final class, as described below. Two extreme approaches for the combination strategy are outlined below:[0003]
• 1. The first approach may accept the decision of the majority of the classifiers as the final decision (decision consensus approach).[0004]
• 2. The second approach can take the decision of the most competent expert as the final decision (most competent expert approach).[0005]
• An intermediate approach involves determining a solution in which a consensus decision is evaluated in terms of the past track records of the experts. Instead of directly accepting the consensus decision, the reliability of each decision is evaluated through various kinds of confidence measures. The decision is either accepted or rejected based on the result of such an evaluation.[0006]
• In a further approach, a Bayesian cost function is minimised over all the decisions given by the experts. The cost function is defined as the cost of making a wrong decision multiplied by the joint probability of occurrence of the respective decisions.[0007]
• None of the above approaches outlined above are rigourously optimal or universally applicable, and can be subject to errors or limitations of one kind or another. Accordingly, it is an object of the invention to at least attempt to address these and other limitations associated with the prior art. In particular, it is an object of the invention to generally improve the classification accuracy of particular decision fusion applications which rely on one of the prior art approaches outlined above.[0008]
SUMMARY OF THE INVENTION
• The inventive concept is founded in recognition that the reliability of a classifier in a decision fusion architecture can vary from sample to sample and from experiment to experiment. The inventive concept involves using the decisions from multiple classifiers in a decision fusion application to make an informed decision as to the classifier which is likely to be correct.[0009]
• More particularly, the inventive concept resides in a recognition that a strategy of assigning confidences to different classifiers in a decision fusion architecture can be used to improve the classification accuracy of a decision fusion application. This inventive strategy is thought to result in improved classification accuracy.[0010]
• Embodiments of the invention involve attempting to optimally adapt the weight given to a particular classifier from sample to sample, which generally results in improved performance compared with prior art approaches. A weight or metric of relative confidence is assigned to every classifier, depending upon its sample confidence and overall confidence (as subsequently described). For each class, an overall score (or likelihood) is calculated which combines individual scores from all classifiers, which allows the class with the highest score (or likelihood) to be designated as the correct class.[0011]
• The invention provides a method suitable for deciding how to classify a sample in one of a number of predetermined classes, the method comprising:[0012]
• (a) associating a weight w[0013]_ijwith each of a plurality of classifiers i which are class models for how to classify a sample j in one of a number of predetermined classes k;
• (b) calculating for each of said predetermined classes k a weighted summation CL[0014]_jkacross said classifiers i of the likelihood l_ijkthat the sample belongs to that respective class k, weighted by the weight w_ij; and
• (c) designating the sample j as belonging to the class k which has an associated weighted summation of likelihoods CL[0015]_jkwhich is greatest in value.
• The invention further provides an apparatus for classifying a data sample in one of a number of predetermined classes, the apparatus comprising: input means to receive data; and processor means for calculating associating a weight w[0016]_ijwith each of a plurality of classifiers i which are class models for how to classify a sample j in one of a number of predetermined classes k, and for designating calculating for each of said predetermined classes k a weighted summation CL_jkacross said classifiers i of the likelihood l_ijkthat the sample belongs to that respective class k, weighted by the weight w_ij. The weight can be derived from a metric of relative confidence in the decision of a respective classifier i. Preferably, this is an L-statistic (linear combination of the order statistic), which represents the statistical separation among the order statistic, preferably log-likelihoods, against the class models for a classifier.
• This determination of relative confidence can be performed in two different ways to calculate two components of weight given to the decision of a classifier i, referred to as sample confidence L[0017]_ijand overall confidence H_i. Preferably, these confidence values of the classifiers i are subsequently used to combine the decisions from the classifiers i to obtain the final decision.
• The L-statistic, for a particular sample j, L[0018]_ijk, can be defined as:
• L_ij=a_il_ijl+a₂l_ij2+ . . . +a_nl_ijn
• where l[0019]_ijkdenotes for sample j and classifier i, the log-likelihood of the kth most likely class is such that the l_ijks form order statistic, that is l_ij1>l_ij2> . . . >l_ijn. The values of a_is define the form of the particular L-statistic L_ijchosen. Preferably, the order statistic used is simply the difference between the log-likelihoods of the two most likely classes k. That is, a₁=1, a₂=−1 and all other a_is=0.
• A cumulative mean H[0020]_iof the sample confidence L_ijover a large number of samples is used to measure the overall discrimination capability of the classifier. It is currently understood that the value of the overall confidence H_iso calculated$H_i=\sum _{j=1}^tL_{\mathrm{ij}}/t$

  
• converges to a constant value which is well separated for different overall confidence levels.[0021]
• Overall confidence for classifier i, H[0022]_i, is computed as cumulative mean or moving average of the L-statistic L_ijover a number of samples j after which it becomes almost constant.
• In the equation directly above t is the number of samples after which the overall confidence value stabilises. H[0023]_iattempts to model some kind of disturbance or noise which is application specific. Typically, such noise degrades the efficiency of the classifier across all classes. For example, in the case of speech recognition, this may be ambient noise (such as car noise, cocktail party noise) present in the audio channel. There may be, of course, some cases in which the amount of noise present in the classifier varies during the experiment.
• For every incoming sample j, sample confidence values L[0024]_ijis are computed for every classifier i. The overall confidence H_ifor the classifiers are updated using L_ij. Preferably, a weight w_ijis assigned to each classifier i as a function of the overall confidence H_iand the sample confidence L_ij. Once weights w_ijfor each classifier are known, each incoming sample j can be classified in a class k by calculating the combined log-likelihood CL_jkfor each class as set out directly below.
• where[0025]
• w_ij=f(L_ij,H_i)
• For the sample j, the class k with the highest calculated combined log-likelihood CL[0026]_jkis finally chosen as the correct class k for sample j. The l_ijkdenotes the log likelihood of sample j for class k using classifier i.
• The invention also includes a computer program product for performing embodiments of the inventive methods described above.[0027]
• Embodiments of the invention can be used in various applications in which decision fusion is conventionally used.[0028]
BRIEF DESCRIPTION OF THE DRAWINGS
• FIG. 1 is a schematic representation of the process involved in reaching a decision in a classification problem, in accordance with an embodiment of the invention.[0029]
• FIG. 2 is a schematic representation of the process involved in determining a weight using a threshold value, in accordance with an embodiment of the invention.[0030]
• FIG. 3 is a schematic representation of computing hardware suitable for performing embodiments of the invention.[0031]
DETAILED DESCRIPTION OF EMBODIMENTS AND BEST MODE
• An embodiment of the invention is described below in the context of an audiovisual speech recognition application which uses decision[0032]${\mathrm{CL}}_{\mathrm{jk}}=\sum _{i=1}^cw_{\mathrm{ij}}*1_{\mathrm{ijk}}$

  
• fusion for classification problems. In this context, there are two relevant classifiers: audio and video.[0033]
• In overview, the classification or recognition process initially involves steps as outlined in FIG. 1. Initially, in[0034]step10, the process involves associating a metric of relative confidence with respective classifiers or class models which predict how a sample should be recognised. The L_ijis calculated instep20 as an L-statistic of the log-likelihoods l_ijk, as detailed below. The moving average H_i, across a suitable number of samples j is then determined instep30. This allows weights W_ito be calculated instep40 for each classifier from H_iand L_ij, according to a suitable function as detailed below. The combined likelihoods across classifiers CL_jkare then calculated instep50 as a weighted summation of the likelihoods of each class, so that the most likely class can then be determined instep60.
• For the speech recognition application decision, the problem can be defined as follows. Given an audio and a video vector corresponding to a particular speech time frame, it is necessary to determine the phone class to which this frame belongs. Phones are modelled as GM (Gaussian Mixture Models) obtained from the training data.[0035]
• Given an audio vector, its likelihood of corresponding to each of the phone classes is computed from the respective classification models. From these likelihoods, the L-statistic is preferably chosen simply as the difference between the first and the second most likely choices. As a result, coefficients a, are used as follows.[0036]
• a₁=1, a₂=−1, all other a_is=0
• A similar computation is also performed for the video vector. The L-statistic is shown as L[0037]_ijin FIG. 2. The cumulative mean of L-statistic, H_iis used here to model the background noise present in the audio channel only, as background noise uniformly degrades the audio recognition rate across all phonetic sounds. Accordingly, the L-statistic L_ijdecreases uniformly in the presence of noise. The combined likelihood of corresponding to a particular phone class is computed as follows.
• CL_i=w_a*l_ai+w_v*l_vi
• Here l[0038]_aiand l_viare log likelihoods for ith audio class and ith video class respectively, w_aand w_vare the weights assigned to the audio and video likelihoods respectively. The phone class with the highest combined likelihood is selected as the correct phone class.
• The weight for audio is determined and, since there are only two classifiers in this case, the weight for video is simply determined as the complement of the weight for audio, as the linear summation of all weights is 1. A threshold at is defined for sample confidence values of audio which are just the L-statistic in this case. First, the class confidence value for audio is checked against its threshold in[0039]step100. If it passes this test, audio weight is computed in step110 as a constant term and a term which is dependent on the overall confidence of the audio channel. If audio fails this test instep120, the constant term in the weight changes.
• Hence this embodiment, function f( ) is implemented as[0040]
• w_ij=f(L_ij, H₁)=f₁(L_ij)+f₂(H₁)
• where f[0041]₁( ) is chosen as a threshold function and f₂( ) is given as
• f₂(H₁)=x₁/(1+exp(x₂*H₁))
• Parameters x[0042]₁and x₂are scalar values that are selected and, if necessary, adjusted to provide good performance. Preferably, sample confidence is used as a confidence measure for a classifier for the current sample being processed. The sample confidence models non-uniform discrimination capability of the classifier across various classes due to the non-uniform dispersion of the clusters in vector space for the data set of the classifier. The sample confidence does not represent the overall discrimination capability of the classifier. A low value of the sample confidence indicates low confidence in its decision for the present sample. Similarly, a high value of the sample confidence indicates a higher confidence in its decision for that sample. The sample confidence for the present sample is preferably represented by the L-statistic for the sample.
• Preferably, overall confidence represents the overall discrimination capability of the classifier across all classes (or clusters). This overall discrimination capability may vary between experiments degraded due to the presence of noise which uniformly degrades the classifier's discrimination capability across all classes. For example, in the case of speech recognition, this may be background noise present in the audio channel.[0043]
• In this application, it is possible to achieve improvements in phonetic classification results using the techniques of the described embodiment of the invention.[0044]
• Computer hardware for performing embodiments of the invention is now described.[0045]
• The described process of classification can be implemented using a computer program product in conjunction with a[0046]computer system200 as shown in FIG. 3. In particular, the process can be implemented as software, or computer readable program code, executing on thecomputer system200.
• The[0047]computer system200 includes acomputer250, avideo display210, andinput devices230,232. In addition, thecomputer system200 can have any of a number of other output devices including line printers, laser printers, plotters, and other reproduction devices connected to thecomputer250. Thecomputer system200 can be connected to one or more other computers via a communication input/output (I/O)interface264 using anappropriate communication channel240 such as a modem communications path, an electronic network, or the like. The network may include a local area network (LAN), a wide area network (WAN), an Intranet, and/or theInternet220.
• The[0048]computer250 includes thecontrol module266, amemory270 that may include random access memory (RAM) and read-only memory (ROM), input/output (I/O) interfaces264,272, avideo interface260, and one or more storage devices generally represented by thestorage device262. Thecontrol module266 is implemented using a central processing unit (CPU) that executes or runs a computer readable program code that performs a particular function or related set of functions.
• The[0049]video interface260 is connected to thevideo display210 and provides video signals from thecomputer250 for display on thevideo display210. User input to operate thecomputer250 can be provided by one or more of theinput devices230,232 via the I/O interface272. For example, a user of thecomputer250 can use a keyboard as I/O interface230 and/or a pointing device such as a mouse as I/O interface232. The keyboard and the mouse provide input to thecomputer250. Thestorage device262 can consist of one or more of the following: a floppy disk, a hard disk drive, a magneto-optical disk drive, CD-ROM, magnetic tape or any other of a number of non-volatile storage devices well known to those skilled in the art. Each of the elements in thecomputer system250 is typically connected to other devices via abus280 that in turn can consist of data, address, and control buses.
• The method steps for are effected by instructions in the software that are carried out by the[0050]computer system200. Again, the software may be implemented as one or more modules for implementing the method steps.
• In particular, the software may be stored in a computer readable medium, including the[0051]storage device262 or that is downloaded from a remote location via theinterface264 and communications channel240 from theInternet220 or another network location or site. Thecomputer system200 includes the computer readable medium having such software or program code recorded such that instructions of the software or the program code can be carried out. The use of thecomputer system200 preferably effects advantageous apparatuses for constructing a runtime symbol table for a computer program in accordance with the embodiments of the invention.
• The[0052]computer system200 is provided for illustrative purposes and other configurations can be employed without departing from the scope and spirit of the invention. The foregoing is merely an example of the types of computers or computer systems with which the embodiments of the invention may be practised. Typically, the processes of the embodiments are resident as software or a computer readable program code recorded on a hard disk drive as the computer readable medium, and read and controlled using thecontrol module266. Intermediate storage of the program code and any data including entities, tickets, and the like may be accomplished using thememory270, possibly in concert with thestorage device262.
• In some instances, the program may be supplied to the user encoded on a CD-ROM or a floppy disk (both generally depicted by the storage device[0053]262), or alternatively could be read by the user from the network via a modem device connected to thecomputer250. Still further, thecomputer system200 can load the software from other computer readable media. This may include magnetic tape, a ROM or integrated circuit, a magneto-optical disk, a radio or infra-red transmission channel between the computer and another device, a computer readable card such as a PCMCIA card, and theInternet220 and Intranets including email transmissions and information recorded on Internet sites and the like. The foregoing are merely examples of relevant computer readable media. Other computer readable media may be practised without departing from the scope and spirit of the invention.
• Further to the above, the described methods can be realised in a centralised fashion in one[0054]computer system200, or in a distributed fashion where different elements are spread across several interconnected computer systems.
• Computer program means or computer program in the present context mean any expression, in any language, code or notation, of a set of instructions intended to cause a system having an information processing capability to perform a particular function either directly or after either or both of the following: a) conversion to another language, code or notation or b) reproduction in a different material form.[0055]
• In the foregoing manner, a method, an apparatus, and a computer program product for are disclosed. While only a small number of embodiments are described, it will be apparent to those skilled in the art in view of this disclosure that numerous changes and/or modifications can be made without departing from the scope and spirit of the invention.[0056]
• It is understood that the invention is not limited to the embodiment described, but that various alterations and modifications, as would be apparent to one skilled in the art, are included within the scope of the invention.[0057]

Claims (13)

We claim:

1. A method suitable for deciding how to classify a sample in one of a number of predetermined classes, the method comprising:

(a) associating a weight w_ijwith each of a plurality of classifiers i which are class models for how to classify a sample j in one of a number of predetermined classes k;

(b) calculating for each of said predetermined classes k a weighted summation CL_jkacross said classifiers i of the likelihood l_ijkthat the sample belongs to that respective class k, weighted by the weight w_ij; and

(c) designating the sample j as belonging to the class k which has an associated weighted summation of likelihoods CL_jkwhich is greatest in value.

2. The method as claimed inclaim 1, wherein the weight w_ijis derived from a metric of relative confidence L_ij, metric of relative which is calculated as an L-statistic, or linear combination of an order statistic, which represents the statistical separation among an order statistic of the classes k for a particular classifier i.

3. The method as claimed inclaim 2, wherein the L-statistic L_ijis of the log-likelihoods of respective classes k for classifiers 1.

4. The method as claimed inclaim 2, wherein the L-statistic L_ij, for a particular sample j, is calculated as: L_ij=a₁l_ij1+a₂l_ij2+ . . . +a_nl_ijn, where l_ijks form order statistic, that is l_ij1>l_ij2> . . . >l_ijnand a₁=1, a₂=−1 and all other a_is=0.

5. The method as claimed inclaim 2, wherein the weight w_iderived from the metric of relative confidence is calculated as a function of (a) sample confidence L_ij, equal to the L-statistic L_ijand (b) overall confidence H_i, the cumulative mean of the sample confidence L_ijover a plurality of samples j.

6. The method as claimed inclaim 5, wherein the overall confidence H_iis successively updated with the sample confidence L_ijof each sample j.

7. A computer program product having a computer readable medium having a computer program recorded therein for deciding how to classify a sample in one of a number of predetermined classes, said computer program product comprising:

(a) code means for associating a weight we with each of a plurality of classifiers i which are class models for how to classify a sample j in one of a number of predetermined classes k;

(b) code means for calculating for each of said predetermined classes k a weighted summation CL_jkacross said classifiers i of the likelihood l_ijkthat the sample belongs to that respective class k, weighted by the weight w_ij; and

(c) code means designating the sample j as belonging to the class k which has an associated weighted summation of likelihoods CL_jkwhich is greatest in value.

8. An apparatus for classifying a data sample in one of a number of predetermined classes, the apparatus comprising: input means to receive data; and processor means for calculating associating a weight w_ijwith each of a plurality of classifiers i which are class models for how to classify a sample j in one of a number of predetermined classes k, and for designating calculating for each of said predetermined classes k a weighted summation CL_jkacross said classifiers i of the likelihood l_ijkthat the sample belongs to that respective class k, weighted by the weight w_ij

9. The apparatus as claimed inclaim 8, wherein the weight w_ijis derived from a metric of relative confidence L_ikmetric of relative which is calculated as an L-static, or linear combination of an order statistic, which represents the statistical separation among an order statistic of the classes k for a particular classifier i.

10. The apparatus as claimed inclaim 9, wherein the L-statistic L_ijis of the log-likelihoods of respective classes k for classifiers i.

11. The apparatus as claimed inclaim 9, wherein the L-statistic L_ij, for a particular j, is calculated as: L_ij=a₁l_ij1+a₂l_ij2+ . . . +a_nl_ijn, where l_ijks form order statistic, that is l_ij1>l_ij2> . . . >l_ijnand a₂=1, a₂=−1 and all other a_is=0.

12. The apparatus as claimed inclaim 9, wherein the weight w_iderived from the metric of relative confidence is calculated as a function of (a) sample confidence L_ij, equal to the L-statistic L_ijand (b) overall confidence H_i, the cumulative mean of the sample confidence L_ijover a plurality of samples j.

13. The apparatus as claimed inclaim 12, wherein, the overall confidence H₁is successively updated with the sample confidence L_ijof each sample j.

Images